Gear machine

ABSTRACT

This invention relates to an improvement in a gear machine comprising an internally toothed outer wheel meshing with an externally toothed inner wheel wherein the outside diameter of the inner wheel is smaller than the root diameter of the outer wheel by at least the height of a tooth. The improvement comprises the tooth flanks of the outer wheel in sections normal to the axis of the outer wheel are defined at least in the upper half of the height of the teeth by equidistant curves from one or two like hypocycloids; THE DIAMETER OF A ROLLING CIRCLE WHICH BY ROLLING ON A BASE CIRCLE THAT IS CONCENTRIC ABOUT THE AXIS OF THE OUTER WHEEL IS A FRACTION OF THE DIAMETER OF THE BASE CIRCLE, WHEREIN THE NUMERATOR AND DENOMINATOR ARE INTEGERS; THE DENOMINATOR OF THE FRACTION IS EQUAL TO THE NUMBER OF TEETH OF THE OUTER WHEEL; IN THE EVENT OF THE NUMERATOR OF THE FRACTION BEING EQUAL TO OR GREATER THAN TWO, THE NUMERATOR AND DENOMINATOR OF THE FRACTION HAVE NO COMMON SUBMULTIPLE; THE EQUIDISTANT CURVE IS RADIALLY OUTSIDE THE CYCLOID OR CYCLOIDS; THE OUTER WHEEL IS HARDENED; THE TOOTH FLANKS OF THE OUTER WHEEL IN THE REGION DEFINED BY THE EQUIDISTANT CURVE ARE GROUND, AND THE TOOTH FORM OF THE INNER WHEEL IN THE REGION OF ENGAGEMENT IS AT LEAST APPROXIMATELY DEFINED BY THE ROLLING OF THE INNER WHEEL IN THE OUTER WHEEL. The invention also includes a method and apparatus for making the gear machine.

O United States Patent 1 1 1111 3,782,040 Harle et al. 1 Jan. 1, 1974 GEAR MACHINE [57] ABSTRACT [75] Inventors: Hermann Harle, '7

Laucherthal/Hohenzollern;Siegfried This invention relates to an improvement in a gear Eisenmann, Sigmaringendorf, both machine comprising an internally toothed outer wheel of Germany meshing with an externally toothed inner wheel wherein the outside diameter of the inner wheel is [73] Asslgnee flursthch r fi s 1 smaller than the root diameter of the outer wheel by g z 2 am e a at least the height of a tooth. The improvement comauc en a ermany vprises the tooth flanks of the outer wheel in sections [22] Filed: Aug. 19, 1971 normal to the axis of the outer wheel are defined at I least in the upper half of the height of the teeth by [21] Appl l73n0 equidistant curves from one or two like hypocycloids; v the diameter of a rolling circle which by rolling on a [30] Foreign Application Priority Data base circle that is concentric about the axis of the Aug. 20, 1970 Germany P 20 41 483.9 Outer Wheel is a fraction of the diameter of the base circle, wherein the numerator and denominator are 52 us. (:1. 51/52 R, 51/67, 51/105 R, integers;

51/287 the denominator of the fraction is equal to the 511 1m. 01 B24b 1/00, B24b 5/36 number of teeth of the Outer Wheel;

[58] Field of Search 51/33 w, 33 R, 52 R, in the event of the numerator 9f the fraetioh being 51 7 105 R, 2 39 DIG 1 equal to or greater than two, the numerator and denominator of the fraction have no common [56] References Cited suhmuhipliei UNITED STATES PATENTS I ortliyeclegiglsdistant curve is radially outside the cycloid 1,486,340 3/l924 Hoke 51/287 the outer, wheel is hardened;

25 the tooth flanks of the outer wheel in the region l'88l'382 (W932 g; SI/287 x defined by the equidistant curve are ground, and the l:964:233 6/l934 Uhlich....... .11.. 51/52 R teeth of the inner wheel in the regte" of 9 0 ||/|9Qg phe|psmn 5 3 R engagement is at least approximately defined by the 3,705.619 12/1972 Holm 51/287 rolling of the inner wheel in the outer wheel. 2,l5l,483 3/1939 Nlchols 5l/52 R The invention also includes a method and apparatus FOREIGN PATENTS OR APPLICATIONS for making the gear machine.

1.078.410 3/1960 Germany 51/010. 1

237,802 5/1945 Switzerland 5l/DlG. l 20 Claims, 13 Drawing Figures Primary Examiner-Donald G. Kelly Attorney-James E. Bryan 220 I A \A I k2 h l 1 Z \-111 1 1e 2 VI VI 1 k\ i \[i ll: 1 I l l t 11 16 17 PATEHTEDJAN H914 3.782.040

8HEET10F INVENTORS HERMANN HARLE SIEGFRIED EISENMANN PATENTEDJAN H I I 3.782.040

' SHEET 3 0? 6 AV AWN/Av AV \V AV/ INVENTORS HERMANN HARLE SIEG FRIED EISENMANN PATENTEDJAN H914 SHEET 5 OF 6 INVENTORS HARLE ATTO NE Y PA EHTEU 1 9M SHEU 6 [IF 6 INVENTORS HER ANN HARLE SIEGFRIED EISENMANN TO NE) GEAR MACHINE This invention relates to gear machines comprising an outer internal gear wheel meshing with an inner external gear wheel, the tooth flanks of each tooth of the outer gear wheel preferably meeting at a line representing the tooth crest (the preferred shape of tooth of the outer gear wheel therefore lacks a flat-topped crest in the accepted sense of the term, instead of which it has a single tip at the line of intersection of the two tooth flanks), and the addendum circle diameter of the inner wheel being smaller than the root circle diameter of the outer wheel by at least the height of a tooth.

The invention is applicable not only to gear transmissions for changing speed or torque but also, in principle, to so-called hydrostatic or volumetric gear pumps or motors. In these machines the gearing functions as a pump when driven, whereas it functions as a motor when a fluid is supplied under pressure.

A major difficulty that arises in the production of gear machines in which an outer internally toothed wheel meshes with an inner externally toothed wheel is that of producing the gearing rationally. Such gear teeth can be produced by shaping by the generating process (the inner wheel also can be generated by milling). This method has the drawback that the pair of gears cannot be hardened if the barest minimum of precision is required.

If the two gears are hardened they distort, particularly the internal gear, and considerable clearances must be provided even if, after hardening, the profiles and the crests of the teeth are ground. The tooth flanks can likewise be ground. However, in the case of the internal gear this cannot be done by using the generating roll process. The tooth flanks of the internal gear can be ground only by using a dividing head, each tooth gap being finish ground before the machine is indexed by the pitch of a tooth and the next gap is ground. This method is also unsuitable for achieving high precision. Moreover, the method is also time-consuming and it is not suitable for major outputs. If the internal gear is ground in this way, the inner wheel can be ground by the generating roll process, provided an involute tooth flank is chosen. Nevertheless, the production problem with respect to the more difficult member of the pair, namely the internal gear, still remains unresolved. lmportant is the fact that the internal gear calls for even higher precision than the inner wheel because during hardening owing to its ring shape the internal gear usually distorts far more than the smaller and more compact inner wheel.

The present invention solves principally the problem of providing a pair of gear wheels for a gear machine comprising an internally toothed outer wheel meshing with an externally toothed inner wheel, in which the tooth flanks of the outer wheel and preferably also of the inner wheel are hardened and ground by the generating roll process.

Owing to the small degree of distortion and the greater ease of compensating faults in pitch and geometry, grinding and possibly even hardening sometimes can be dispensed with for the inner wheel. Moreover, the inner wheel can be ground with the aid of a dividing head more easily and with fewer faults. If a sufficiently hard steel is used for the inner wheel, it also can be shaped and shaved. lts higher wear compared with the outer wheel can be more readily accepted because the inner wheel, when not hardened but merely shaped or milled, is fairly easy to produce and hence replaceable at less expense. Nevertheless it is preferred that the inner wheel should likewise be hardened and ground. In the case of more exacting requirements relating to .precision and life of the inner wheel, this is an unavoidable necessity.

For solving the above-described problem the invention proceeds from the thought that the teeth of the outer wheel should have a tooth flank profile that can be ground by the generating roll process. The teeth of the inner wheel can then be finish machined in a ma chine simulating the rolling of the inner wheel in the outer wheel, by shaping or milling, but preferably by grinding.

In the gear machine proposed by the invention, the gear flanks of the outer gear viewed in sectional planes normal to the gear wheel axis, at least in the upper half of the height of the tooth and preferably in the upper four-fifths, are defined by equidistant curves from one or two like hypocycloids. The diameter of the circle generating the cycloid and cycloids by rolling on a base circle concentric about the outer wheel axis is a fraction of the base circle diameter. The numerator and denominator of the fraction are integers, the denominator of the fraction equals the number of teeth of the outer gear wheel, and when the numerator of the fraction equals or is greater than two, the numerator and denominator of the fraction have no common submultiple. The equidistant curve is radially outside the cycloid and cycloids, the outer wheel is hardened (the expression hardened is here intended to embrace not only materials that have been hardened by an appropriate treatment but also materials that by nature are so hard that they cannot be machined otherwise than by grinding), the tooth flanks of the outer gear wheel are at least and preferably ground in the zones defined by the equidistant curves, and the tooth profile of the inner gear wheel in the region of mesh is at least approximately defined by the rolling of the inner wheel in the outer wheel.

The preferred material for the outer wheel and the inner wheel is steel.

Hence, if the outer wheel is to have 9 teeth, for example, then the diameter of the rolling circle theoretically may be any fraction of the base circle from 1/9 to 8/9 with the exception of three-ninths and six-ninths. Since in the case of one-ninth and eight-ninths the resultant teeth are arcuate, these values represent Eaton gears. For other gears only the values two-ninths, four-ninths, five-ninths and seven-ninths for the diameter of the rolling circle are suitable. Since it can be shown by mathematical calculation that two rolling circles having diameters whose sum is equal to the diameter of the base circle generate the same cycloid, only two cycloids are suitable, namely one having a rolling circle diameter of two-ninths or seven-ninths and the other having a rolling circle diameter of four-ninths or fiveninths. In the latter case the height of the tooth can be kept low and the gap width sufficiently wide by choosing a distance from the cycloid for the equidistant curve that is sufficiently large.

In the case of a wheel having 20 teeth, for example, the available choice of a cycloid is already substantially wider because of the greater number of teeth. The ratio of the diameter of the rolling circle to that of the base circle can here assume the values one-twentieth, threetwentieths, seven-twentieths, eleven-twentieths, thirteen-twentieths, seventeen-twentieths, and nineteentwentieths. Owing to the equivalence of one-twentieth and nineteen-twentieths, of three-twentieths and seventeen-twentieths, of seven-twentieths and thirteentwentieths as well as of nine-twentieths and eleventwentieths there are therefore four possible cycloids.

Where it was stated that the tooth flanks were to be defined by an equidistant curve from one or two like hypocycloids, this is so because, as will be latter explained, it is desirable that all the right-hand tooth flanks should be defined by an equidistant curve from one cycloid and all the left-hand tooth flanks by an equidistant curve from another like cycloid displaced by a small angle in relation to the first. Definition by an equidistant curve from one cycloid is possible and is in fact even preferable when the ratio of the diameter of the rolling circle to that of the base circle is l/n or (n-l )/n (n being an integer).

Where hereinafter in the course of further explanations of the underlying principle reference is made to only one cycloid it is to be understood that this includes the use of two cycloids. The omission in the explanations is merely to avoid confusing the issue.

A curve of constant distance or an equidistant curve from a hypocycloid is here understood to be the envelope curve of all circles of like diameter having their centers on the hypocycloid.

The generation of the tooth flanks by an equidistant curve from a hypocycloid enables the precise desired tooth shape to be ground in apparatus in which a grinding element moves along a hypocycloidal path in relation to the outer wheel and the radius of the element is equal to the distance of the equidistant curve from the hypocycloid. It is technically possible to generate movement along a hypocycloid because a hypocycloid of the kind the invention employs can be generated in the simplest case by rolling a gear wheel having a pitch circle equal to the rolling circle of the hypocycloid inside a fixed outer internal gear having a pitch circle equal to the base circle of the hypocycloid. Nevertheless, a different method that will be later described is preferred.

However, for achieving the object of the invention the described choice of the tooth flanks is not yet sufficient. To enable such tooth flanks to be ground by a generating roll process it is necessary that at least all the left-hand or right-hand tooth flanks and then all the right-hand respectively left-hand tooth flanks or possibly all the tooth flanks should be ground in one continuous operation in which the blank need be clamped up only once. This could be done fairly easily only if the ground part of each tooth were defined by a single cy cloidal arc. This results in the generation of a so-called Eaton gear in which each tooth has the shape of an equidistant curve from a hypocycloid. This type of gear is used in gear pumps having an internally geared wheel. Mesh in the region of the crests is unsatisfactory because of the clearances that are needed between the teeth. In the majority of cases the above-mentioned condition of an ogive tooth" must be observed or at least a tooth form having steeper flanks must be employed than would be possible by defining both tooth flanks of a tooth by a common cycloidal are. This condition again requires that the equidistant curve from the hypocycloid between two contact points of the cycloid and the base circle should define the remote tooth flanks of two neighboring or still more widely separated teeth. If this is to be achieved in one operation the cycloid must close upon itself in more than one revolution.

The condition that the cycloid must be closed is naturally obvious. That the cycloid must close upon itself in more than one convolution means that the cycloid is generated by the rolling of a generating circle in which the point tracing the cycloid will not reach its starting position until after having performed at least two complete revolutions about the center of the base circle. This is also the preferred and simplest embodiment of the invention. If the cycloid reaches the starting point after an even number of revolutions, the number of teeth of the outer wheel must be odd. If the cycloid is back where it began after an odd number of revolutions the number of teeth of the outer wheel must be even.

By correctly selecting the ratio of the diameter of the rolling circle to the diameter of the base circle within the above described limits the diversity of choice increases with an increasing number of teeth. In the case of smaller tooth numbers, such as seven teeth for the outer wheel, there is not much room for choice. The diameter of the rolling circle to that of the base circle must be either one-seventh, two-sevenths, threesevenths, four-sevenths, five-sevenths or six-sevenths. If an Eaton tooth is not desired, only the two possible cycloids defined by the fraction two-sevenths respectively five-sevenths and three-sevenths respectively four-sevenths remain.

The equidistant curve, viewed from the inside of the cycloid that closes upon itself in more than one revolution, must run outside the cycloid since it is in fact the envelope curve of the grinding wheel in its path when it grinds the tooth flanks. The minimum condition for performing the method according to the invention is therefore that the tooth flanks of the outer wheel should be ground in the region defined by the equidistant curve. The tooth flanks in the region near the root where high precision is less important then may be reground by using a dividing head. However, such a procedure is not preferred. The crest of the tooth can be separately ground unless, as is preferred, it is formed by a line parallel to the axis of the outer wheel.

Preferably both gear wheels may be hardened. More particularly, in mesh with the cooperating wheel unground parts of the tooth flanks should not make contact, nor should the tooth crests make contact with the bottom of the gaps between the teeth.

Moreover, preferably all the teeth should have a symmetrical contour, as is conventional, and it is also preferred that the number of teeth of the outer wheel and of the inner wheel should have no common submultiple. This is an advantage in production as well as for ensuring smooth running.

The point on the rolling circle generating the hypocycloid or hypocycloids is preferably located on the circumference of the rolling circle. Any offsetting towards the inside or outside of the rolling circle normally should be slight.

In order to avoid unfavorable proportions, the tooth height of the outer wheel, measured from the base circle, preferably should be less than 30 per cent of the radius of the base circle. Preferably, the height of the teeth of the outer wheel from the base circle should be less than 25 per cent but exceed 5 per cent ofthe radius of the base circle.

Moreover, it is also preferred that the equidistant curve defining the left-hand tooth flanks should clear the right-hand tooth flanks and the equidistant curve from the cycloid defining the right-hand tooth-flanks should clear the left-hand tooth flanks. This ensures that the grinding element will make contact with only one tooth flank at a time, an advantage from the production point of view. The desired result can be relatively easily achieved by first grinding all the left-hand tooth flanks, by then slightly turning the outer wheel about its axis or shifting the grinding disc far enough for the latter to engage the right-hand and left-hand tooth flanks. In this procedure all the left-hand tooth flanks are defined by the equidistant curve from a cycloid which is angularly displaced from the cycloid for generating the right-hand tooth flanks. This is thus a case in which two cycloids are used. It is quiate possible to do without this condition. However, in the latter case the grinding wheel will be called upon to grind at two points simultaneously when it passes through the cycloid cusps. Nevertheless, this can be avoided by slight relief of the tooth flank adjoining the root during roughing and prior to hardening. However, the supporting part of the tooth flank will thus be somewhat reduced.

If it is desired to observe the condition that was described as advantageous at the beginning of the last paragraph, the distance of the equidistant curve from the cycloid preferably should be slightly less (preferably 5 to 20 per cent and more, particularly about per cent less) than half the linear distance between the ground zones of facing flanks of neighboring teeth of the outer wheel where these zones are closest together.

As a general rule the distance between two facing tooth flanks of neighboring teeth of the outer wheel, measured on the base circle, will be roughly equal to the distance between the tooth flanks of the same teeth on the base circle.

The tooth flanks need not be ground down to the root. Frequently it will be sufficient if the tooth flanks are ground from the tip of the tooth to the base circle of the cycloid or cycloids. The depth of engagement is then limited to that part of the tooth flanks that extends between the tip of the tooth and the base circle. The other parts of the tooth flanks naturally must be machined out sufficiently to prevent contact with the teeth of the inner wheel. When the teeth of the outer wheel have crests with flat tops in the circumferential direction of the addendum circle it may be advantageous to provide tip relief prior to hardening and grinding.

As is generally conventional, the shape of the tooth flanks in the inner wheel in a gear machine according to the invention is defined only in principle by the rolling of the inner wheel in the outer wheel. Otherwise no clearance between the teeth would be present.

Preferably at least the upper half of the tooth flank profile of the inner wheel is generated by rolling the inner wheel in an auxiliary outer wheel which has tooth flanks that at least in their upper halves are defined in sections normal to the axis of the outer wheel by arcs of circles. These arcs touch the equidistant curve defining the tooth flanks of the outer wheel at least approximately at the tip of the tooth. The radius of the arcs which should envelop the equidistant curve or curves as closely as possible is equal to the radius of curvature of the equidistant curve at the point of contact or slightly greater. The relatively remote tooth flanks facing the cusps of the embracing cycloidal arc of two teeth of the auxiliary outer wheel are defined by a common circular-arc at least in the upper half of the teeth. The relatively remote tooth flanks are the end flanks of a group of adjacent teeth, equal in number to the denominator of the above-mentioned fraction. At least the upper half of the tooth flanks of the inner wheel is ground. Such a design has the great advantage that the grinding of the tooth flanks can be accomplished with the aid of a grinding means that is deflectable about an axis parallel to the grinding element, as will be elaborated upon in detail as the description proceeds.

In the alternative, a relatively complicated arrangement is necessary for grinding the tooth flanks of the inner wheel. Yet another possibility of grinding the tooth flanks of the inner wheel consists in grinding them with the aid of a dividing head. in the case of the inner whee] this is more acceptable than in the case of the outer wheel. However, the tooth contour described in the first part of this section, which can be produced by the generating roll process, is preferred.

The invention also relates to a method of grinding the preformed blank of an outer wheel for a gear machine according to the invention.

According to the invention this consists in rotating the outer wheel about its axis at a predetermined speed, superimposing upon this rotation about the axis of the outer wheel a second rotation about a second axis which is parallel to the axis of the outer wheel and located at a distance therefore equal to the radius of the base circle diminished by the radius of the rolling circle, the ratio of the speed of rotation of the outer wheel about its axis to the speed of the superimposed rotation being equal to the ratio of the distance to the radius of the base circle of the cycloid. Both rotations proceed in the same direction if the rolling circle is the smaller of the two possible rolling circles, and in the contrary directions if the rolling circle is the greater of the circles. Consequently, the axis of the grinding spindle which runs parallel to the second eccentric axis is moved perpendicularly to its axis only for the purpose of infeeding the grinding element as material is removed from the interior of the outer wheel. This infeeding motion is in a direction away from the second axis. By proceeding in this way the grinding spindle is so conducted in relation to the outer wheel blank that the circumference of the grinding element defines the desired equidistant curve from a hypocycloid.

Conveniently the rotating grinding spindle is reciprocated in the axial direction during grinding, as is conventional.

If it is desired to generate an outer wheel in which each equidistant curve from the cycloidal arc makes contact with only one tooth flank (cycloidal arc is here understood to be the arc of a hypocycloid between two consecutive radial end points), i.e., in the event of the grinding spindle not being desired to grind two tooth flanks at the same time when its axis passes through the cusps of the cycloid and appropriate clearance has not been machined into the blank, then it is preferred, after finish grinding all the left-hand or right-hand flanks and returning the grinding spindle into starting position to turn the outer wheel about its axis, without rotation of the second axis, a sufficient distance in relation to the grinding spindle for the latter now to grind the righthand and left-hand tooth flanks.

Instead of turning the outer wheel blank, the grinding spindle could just as well be displaced a corresponding distance along a line normal to the center axis of the tooth gap in which the grinding spindle happens to be. Thus shifting the grinding spindle is simpler than to turn the outer wheel blank.

The invention also relates to a method of grinding the tooth flanks of the inner wheel of the gear machine according to the invention. This method comprises rotating the inner wheel about its axis at a given speed, superimposing upon this speed about the axis of the inner wheel a second rotation at a different speed about a second axis extending parallel to the axis of the inner wheel at a distance equal to the length of the difference between the radii of the pitch circles of outer and inner wheel, the ratio of the speed of the inner wheel about its axis to that of the superimposed rotation being equal to the ratio of the difference between the radii of the pitch circles of the outer and the inner wheel to the radius of the pitch circle of the inner wheel, both rotations being in contrary directions and the tooth flanks being machined during this motion by the generating roll process.

However, if it is desired to use a gear shaper for the inner wheel, then machining is preferably performed by a shaping tool having the profile of at least part of the teeth of the outer wheel and being reciprocated parallel to the axes of rotation without moving perpendicularly to the second axis, apart from the in-feed necessary to allow for the progressive removal of material.

If the flanks of the inner wheel are to be ground, machining preferably is done with the aid of a grinding spindle which is parallel to the axes of rotation. The grinding spindle is reciprocated along an arc ofa circle normal to the axes of rotation, the arc enveloping the equidistant curve in the region in which the tooth flanks are to be ground. The swivelling radius through the grinding spindle passes continuously through a point which rotates about the second axis at the same speed as the latter, and which is at a distance from the second axis equal to the radius of the pitch circle of the outer wheel.

The process can be so performed that after a lefthand or right-hand tooth flank has been ground the grinding spindle is withdrawn in the direction of its axis out of engagement with the inner wheel, that after having traversed the gaps between the teeth of the aforementioned group the grinding spindle is reengaged with the inner wheel to grind the left-hand and right-hand tooth flank of the last tooth of the group and so forth and that finally, after all the left-hand or right-hand tooth flanks have been finish ground, either the direction of rotation of the two axes is reversed or merely the inner wheel is turned over and all the right-hand and left-hand tooth flanks ground. This procedure has the advantage that every useful number of teeth on the inner wheel can be ground in this way.

An alternative procedure for grinding an inner wheel wherein the ratio of the odd number of teeth to the number of teeth of the generating outer wheel equals the ratio of the rolling circle of the cycloid for generating the teeth of the outer wheel to the base circle of the cycloid, consists in axially withdrawing the grinding spindle in a direction contrary to the curcumferential direction of the inner wheel out of engagement with the inner wheel when the flanks and tip of a tooth have been ground by traversing a complete arc ofa circle enveloping a cycloidal arc embracing only one tooth gap in the outer wheel, returning the grinding spindle across the following tooth and reengaging the same with the inner wheel for grinding the next tooth but one, the cycle being repeated until the grinding of the inner wheel has been completed. This process has the advantage of all tooth flanks and tips of the inner wheel being machined without repositioning the inner wheel and without undesirable clearance being created in the machine.

In both these procedures the shape of the ground tooth flanks of the inner wheel does not conform precisely with the theoretical shape required by the corresponding outer wheel. In fact, the tooth flanks of the outer wheel generating the inner wheel (in the geometrical meaning of the word), which as such have the shape of part ofthe equidistant curve froma hypocycloid are replaced by a shape approximating arc of circles. However, the approximation is very good and the apparatus need not be complicated. An essential feature of this procedure is that the arc of a circle replacing a portion of the equidistant curve may touch the latter at only one point and must otherwise extend between the equidistant curve and the arc of the hypocycloid to which the equidistant curve relates. The distance of this arc of a circle from the equidistant curve naturally should be everywhere as small as possible. Furthermore, the arc of a circle should embrace two tooth flanks that are relatively remote and each should face one adjacent cusp of the same cycloidal arc.

The invention also relates to apparatus for performing the above-described methods of producing both the outer wheel and the inner wheel. In the apparatus for grinding the outer wheel one of two relatively eccentric parts of an eccentric shaft is rotatably mounted in a baseplate and the eccentricity of the two parts of the eccentric shaft is equal to the difference between the radius of the base circle and the radius of the rolling circle of the cycloid. The free part of the eccentric shaft rotatably carries a table to which the outer wheel can be clamped and the eccentric shaft and the rotatable table are driven through gearing at different speeds. The ratio of the speed of rotation of the eccentric shaft to the speed of rotation of the table rotatably mounted on its eccentric part is equal to the ratio of the radius of the base circle to the difference between the radius of the base circle and the radius of the rolling circle of the cycloid. A grinding means which is fixed in relation to the baseplate is provided having a grinding spindle extending parallel to the axes of the eccentric shaft and the grinding spindle is radially displaceable in relation to the bearings of the eccentric shaft in the baseplate.

When an internal gear wheel is clamped up on the table, a grinding means attached to the baseplate performs a movement in relation to the outer wheel that rotates with the table, which movement follows the cycloid defining the shape of the teeth of the wheel. In the apparatus for machining the inner wheel, one part of an eccentric shaft comprising two relatively eccentric parts is rotatably mounted in a baseplate of the machine, and the eccentricity of the two parts of the eccentric shaft equals the difference between the radii of the pitch circles of outer wheel and inner wheel. The portion of the eccentric shaft not mounted in the baseplate of the machine rotatably carries a working table, and the eccentric shaft and the working table are drivable at different speeds. The ratio of the speed of the eccentric shaft to the speed of the table equals the ratio of the radius of the pitch circle of the inner wheel to the difference between the radii of the pitch circles of the outer wheel and the inner wheel, and the baseplate carries means for machining the tooth flanks of the inner wheel.

For grinding the tooth flanks of the inner wheel, the apparatus is conveniently so arranged that the means for machining the tooth flanks of the inner wheel comprise a grinding wheel which is deflectable on an arm about an axis which is fixed in relation to the baseplate and parallel to the axis of the eccentric shaft, and this axis is offset from the eccentric shaft hearings in the baseplate at an appropriate distance for a circular are about the axis to approximate and envelop at least one and preferably two tooth flanks of the outer wheel. The grinding wheel is so mounted on the arm that its envelope curve during deflection about the axis traverses the circular arc and means are provided for moving the grinding wheel in its axial direction for engaging the same with and disengaging it from the teeth of the inner wheel. The arm carrying the grinding wheel is slidably guided in ways rotating synchronously with the eccentric shaft about an axis parallel to one of the axes of the eccentric shaft and the axis of rotation of the ways is offset from the axis of the bearings of the eccentric shaft in the baseplate by a distance equal to the radius of the pitch circle of the outer wheel. Naturally, there is also the possibility, which may be useful in practice,- of a kinematic reversal in which the axis of the grinding spindle together with the means for axially moving the grinding spindle are fixed and the baseplate together with the rotatable parts which it supports swing in a circular arc about the swivel axis.

Generally, it should be observed that the gear teeth of the proposed gear machine naturally must also satisfy the known laws andneeds that apply to all gearings. For instance, the necessary tooth flank clearances and the necessary tip clearances must be provided.

The principles relating to minimum number of teeth and maximum number of teeth in working pairs consisting of an internal gear and an external gear naturally likewise apply to the present invention.

Embodiments of the invention will now be illustratively described with reference to FIGS. 1 to 12. In this context it should be noted that the following description of the apparatus according to the invention is considerably simplified to facilitate an understanding of the basic principles that underlie the invention.

In the drawings FIG. I is a schematic representation of a gear machine according to the invention in a section through the axes of the inner and outer wheels,

FIG. 2 is a section taken on the line II of FIG. 1,

FIG. 3 illustrates the geometrical relationships existing in an outer internal gear wheel according to the invention,

FIG. 4 is a schematic representation of an apparatus for grinding an outer wheel according to the invention,

FIG. 5 is the eccentric shaft of the apparatus according to the invention,

FIG. 6 is a section taken on the line VI VI of FIG.

FIG. 7 is a schematic representation of an apparatus for shaping the flanks of an inner wheel,

FIG. 8 is a schematic drawing illustrating the geometrical relationships that exist when grinding an innner wheel according to the invention with the aid of a grinding spindle that is movable along an arc of a circle,

FIG. 8a is a schematic representation of the geometrical relationships applying to a modified form of the principle underlying FIG. 8, shown on a smaller scale than FIG. 8,

FIG. 9 is a schematic representation of an apparatus for grinding the flanks of an inner wheel according to FIG. 8,

FIG. 10 illustrates a cycloid which closes upon itself after two revolutions as well as the corresponding equidistant curve for the generation of the teeth of an internal gear having seven teeth,

FIG. 11 illustrates a case of a greater number of teeth, i.e., 21 teeth, and

FIG. 12 is an example of an outer wheel having 16 teeth in which the generating point on the rolling circle returns to its starting position after three complete revolutions around the base circle.

The gear machine illustrated in FIGS. 1 and 2 has a divided casing 3 in which an outer interenal gear wheel .1 is rotatably mounted. An innner external gear wheel 2 is secured on a shaft 4 which extends through two bearing bushes in the casing 3. If in this arrangement entry openings 5 and 6 are provided as indicated in FIG. 2 and the inner wheel is driven, then the machine will function as a gear pump. Alternatively, if a pressure medium is introduced through one of the openings, the machine will run as a motor, shaft 4 being the output shaft. If the casing 3 is mounted in bearings, not shown, so that it is rotatable about an axis concentric with the shaft 4 and the casing 3 is driven, then the arrangement can be used as a reduction gearing having a considerable reduction ratio. Gear transmissions, pumps and motors of the described kind are well known in the art.

As already explained, the basic problem in such machines is that of satisfactorily producing precisely worked and preferably hardened gear teeth.

The gear teeth of the outer wheel will be hereinafter described with reference to FIG. 3. In the internal gear wheel shown in the drawing the base circle F has a radius rF. A hypocycloid H for defining the tooth flanks in generated by the rolling of a rolling circle R of radius rR on the base circle F. A point P on the rolling circle generates the cycloid. The same cycloid is also generated by a rolling circle R of radius rR' rF rR rolling on the base circle in the opposite direction. In the illustrated example the outer wheel 1 has nine teeth. Consequently, as has already been described above, the radius of the rolling circle R must be two-ninths or fourninths or that of R must be seven-ninths or five-ninths of the radius of the base circle unless Eaton gears are to be generated. As will be understood from FIG. 3 the height of the teeth already might be excessive in the case of a 4/9ratio and for satisfactory mesh the teeth could not have sharp tips but would require crests with landsIThis would be a drawback for the inner wheel which necessarily can have only a small number of teeth. Consequently the proportion of 7 9 or 2 9 will be chosen for the radius of the rolling circle rR to that of the base circle rF. For generating the teeth of the internal gear the axis of the grinding disc 7 is therefore conducted along the line of the hypocycloid H which closes upon itself in two revolutions. Hence the periphery of the grinding wheel 7 which has a radius rS will move along a curve E which is equidistant from the hypocycloid H. It will be further understood from the drawing that this equidistant curve does not contact both the relatively remote flanks 1a and 1b of two neighboring teeth of the internal gear. It makes contact merely with the right-hand flank lb of one tooth (viewed from the center of the internal gear) so that this flank will assume the exact shape of the equidistant curve. The grinding wheel 7 clears the left-hand flanks la of the teeth. Consequently, the reactive forces acting on the grinding wheel during grinding are reduced. Moreover, when the grinding wheel wears it can be infed towards the right-hand tooth flank. Another matter that will be understood from the drawing is that the internal gear blank has beenrough machined before being ground and hardened in such a way that in a region outside the base circle the grinding wheel will run clear. In this region, which is not ground, no contact occurs between the internal gear and the inner wheel. The teeth are therefore ground only in the region marked 1d.

From this short explanation with reference to FIG. 3 it already will be clear that by proceeding according to the invention, i.e., by conducting the axis of a grinding spindle along the line of a hypocycloid of the above defined kind it is possible to grind an unexceptional tooth flank. When in FIG. 3 all the right-hand tooth flanks have been ground it is sufficient for instance to index a table to which the internal gear 1 has been affixed through a suitable angle for all the left-hand tooth flanks to be reached by the grinding wheel. In order to facilitate an understanding of the process, this description is based on the tacit assumption that the grinding wheel does not wear and need not be fed to the work, and that the entire tooth flank is ground in one traverse. In practice this naturally will not be the case and the grinding wheel must have an exactly defined diameter during the final traverse in which substantially no further material is removed. Moreover, the entire depth of material that requires removal is naturally in practice removed in a large number of passes. Consequently, the grinding wheel must be fed radially outwards in the internal gear during the machining process. These details, which are well understood in grinding technology, need not here be specially described to avoid obscuring the relevant issues.

For grinding an internal gear wheel of the contemplated kind, apparatus can be used such as that schematically shown in FIGS. 4 to 6. In this context it may be repeated that FIGS. 4 to 6 are merely schematic drawings, the practical design of the apparatus naturally being very much more complicated.

The apparatus comprises a baseplate 10 which in a central bearing bush ll, rotatably mounted to rotate about an axis Z, carries the bottom part 12a of an eccentric shaft 12. The eccentricity between the two parts 12a and 12b of the eccentric shaft 12 equals the length of the radius rF of the base circle F less the length of the radius rR or rR' of the rolling circle R respectively r', rR. The axis of a grinding element 7 thus moves along a hypocycloid H in relation to the internal gear 1 that is to be ground. Secured on the upper part 12b of the eccentric shaft 12 is a disc 13. This disc 13 carreies two rotatable pinions 14 and 15. The two pinions are not only in mutual mesh; the pinion 14 which is closer to the eccentric shaft is also in mesh with gear teeth 16 on the bearing bush 11 of the baseplate 10, whereas the pinion 15 that is remote from the eccentric shaft meshes with gear teeth 17 in a worktable 18. The worktable 18 is rotatably mounted on the upper part in FIG. 4 of the eccentric shaft 12. The gearing 17 is concentric about the upper part of the eccentric shaft.

The apparatus is driven through a gear wheel 19 which is rotatable about the bearing bush 11 and drivable by a motor 20 as indicated in dot-dash lines. The shafts of te two pinions l4 and 15 project into this gear wheel 19 so that rotation of the gear wheel 19 causes part 12b of the eccentric shaft 12 that is offset with respect to the bearing 11 to rotate at the same speed as the gear wheel 19. The transmission ratio of the gear wheel 16 to the gear wheel 17 is so selected that the speed of the worktable 18 bears the same proportion'to the speed of the eccentric shaft 12 as the base circle diameter reduced by the diameter of the rolling circle to the diameter of the base circle. The hands of rotation are identical. Therefore, assuming that the internal gear wheel 1 that has been clamped up on the table 18, in a manner not shown, is to receive 2] teeth and that the hypocycloid H is intended to close upon itself after four revolutions of the rolling circle around the interior of the base circle, then the ratio of the speed of the table 18 to the speed of the eccentric shaft 12 must be 4 21 if the directions of rotation are the same 17 21 if the directions of rotation are opposed. Affixed to the baseplate 10 is a support 21 for the grinding spindle 22 which revolves about its axis 22a, and which carries a cylindrical grinding element 7. In the illustrated embodiment the grinding spindle is not movable. It is driven by a motor 23. Naturally in actual practice the arrangement must be provided with means for moving the grinding spindle 22 in FIG. 4 in the plane of the paper from left to right in order to feed the grinding spindle to the work as material is removed. Moreover,

in practice the apparatus must be provided with means for reciprocating the grinding spindle in oscillatory motion parallel to its axis to generate exactly cylindrical tooth flanks.

Assuming that the grinding spindle 22 runs and that the drive 20 is activated, then the internal gear 1 in the drawing will perform movements in relation to the axis 22 of the grinding spindle which are equivalent to conducting the axis of the grinding spindle relative to the internal gear 1 along the hypocycloid H. Embodiments of the proposed apparatus are also possible in which, for example, the internal gear 1 is kept stationary and the grinding spindle is made to perform the necessary motions. However, mechanically this latter arrangement is more complicated. The important point from the point of view of the invention is that it is possible with the aid of eccentric drives to superimpose upon a slow rotation a rapid rotary motion of small radius for the generation of a hypocycloid.

For mass production apparatus of the described kind naturally may be fitted with an eccentric shaft and gearing that is fixed and cannot be adjusted.

If a single machine is intended to grind different numbers of teeth in different internal gears, a different arrangement will in practice be better. In such a case the lower part of the eccentric shaft 12 in FIG. 4 may be attached to the upper part of the eccentric shaft in such a way that it can be displaced in ways replacing the disc 13 for the purpose of varying the eccentricity of the eccentric shaft. Moreover, the eccentric shaft and the table with advantage may be driven through a change speed transmission which separately drives on the one hand the eccentric shaft and on the other hand the table 18 in such a manner that the transmission ratio is selectably variable. For example, such a change speed transmission to mention only one possibility might be arrrnged on the one hand to drive the gear wheel 19 which would then be directly attached to the ways that replace the disc 13. Another output of the change speed transmission then could be arranged to operate through an intermediate gear mounted concentrically with the bottom part of the eccentric shaft 12 and cooperating with a corresponding gearing on the table 18, for instance in the form of an internal gear ring. Diverse possibilities are available.

The simplest method of generating a precise set of gear teeth in the inner wheel will be hereunder described with reference to FIG. 7. The invention is here based on the fact that each point of the inner wheel when correctly meshing with the interal gear likewise describes a hypocycloidal curve. The pitch of the internal gear is the base circle for the generation of this latter hypocycloid which will be hereinafter referred to for the sake of differentiation as the inner wheel cycloid, since the pitch circle of the inner wheel rolls on the pitch circle of the internal gear. The pitch circle diameter of the inner wheel is the rolling circle of the inner wheel cycloid. In this context it should be pointed out that the expression pitch circle is intended to be the rolling circle between cooperating gears. Since in the generation of a hypocycloid the term rolling circle is likewise employed, the present specification will confine itself to referring to the latter merely in connection with the generation of cycloids.

Based on the fact that during the rolling motion of the inner wheel in the internal gear 1 every point on the pitch circle of the inner wheel will generate an inner wheel cycloid, it is possible for simulating the rolling motion of the inner wheel in the internal gear to make use of apparatus which in principle is of the same construction as that illustrated in FIGS. 4 to 6. However in FIG. 7 this arrangement is shown, as it were, in reverse. In other words, the baseplate 10 in FIG. 4 is provided with a supplementary cover plate 30 which carries support means for clamping up the inner wheel 2. However, otherwise the arrangement is the same although the transmission ratios and the eccentricity are different. In the apparatus according to FIG. 7 in which the table 18 of the apparatus according to FIG. 4 now forms the baseplate 18 and the baseplate 10 in the apparatus according to FIG. 4 is the table, the ratio of the speed of rotation of the eccentric shaft about the axis 52 to the speed of rotation of the baseplate 10, forming the table, about the axis I equals the ratio of the pitch circle radius of the inner wheel to the difference betweeen the pitch circle radii of the internal gear and the inner wheel. The eccentricity of the eccentric shaft equals the difference between the pitch circle radii of the internal gear and the inner wheel. By now affixing to the table 18, here forming the base, a support 33 for a vertically reciprocating shaping tool drive 32 which carries a segment 34 of an internal gear as the tool, and by driving the apparatus from the motor 35 attached to the base 10 through drive means indicated in dotted lines, the inner wheel 2 will be made to perform the same rolling motion in relation to the segment 34 of the internal gear which the finished inner wheel would perform in relation to the finished internal gear 1. The shaper mechanism 32 fitted with the internal gear segment 34 can now machine the teeth of the inner wheel in the usual and conventional manner.

The above-described method is independent of the number of teeth of the inner wheel. For instance, assuming that the inner wheel has only two teeth, a form which may be of little interest in actual practice, the ratio of the pitch circle radius of the inner wheel to the difference between the pitch circle radii of internal gear and inner wheel would be 2/7 if the internal gear hasflse If einwwlzefl ha ssx nlse r ample, a more ususal arrangement in prictice, the above ratio will be 7/2. The negative sign indicates that the directions of rotation of the eccentric shaft and of the inner wheel are contrary.

In the two assumed cases the eccentricities of the eccentric shaft are likewise different. In the first case the eccentricity is large because the difference between the pitch circle radii is large. In the second case with seven teeth it is small because the difference is also small.

There is, however, a limitation which must be considered. If the internal gear 34 has only a few teeth, the ratio of the number of teeth of the innner wheel to the number of teeth of the internal gear must have no common submultiple. Only when this is the case will all the teeth of the inner wheel satisfactorily roll on the internal gear segment 34, since otherwise there is no certainty that each tooth of the internal gear will in the course of consecutive revolutions engage every tooth gap of the inner wheel. If this stated condition is not fulfilled, the shaping tool must comprise a sufficiently large segment of teeth of the same shape as the internal gear. The number of teeth in this segment must be sufficient for each gap between neighboring teeth of the inner wheel to perform a complete rolling motion over at least one tooth of the shaping tool.

Although the above-described apparatus permits very accurate inner wheels to be generated it is still not possible to harden these inner wheels without running the risk of distortion. In order to overcome this difficulty the contours to which the tooth flanks of the inner wheel are ground are arcs of circles.

The geometrical reasons that underlie this step are illustrated in FIG. 8. The drawing shows several of the teeth of the inner wheel 2 as well as the contours of part of the internal gear 1. The latter has a pitch circle Ta having a raius ra. The pitch circle Ti of the inner wheel has the radius ri. The momentary point of contact of the two pitch circles is at B. The center of the inner wheel is always located on the line connecting the center of the internal gear and this point of contact. The rolling motion of the inner wheel in the internal gear can be readily simulated by mounting the inner wheel on a table, as already described with reference to FIG. 7, which rotates about the center of the inner wheel. This table is itself mounted on an eccentric shaft which rotates about the center of the internal gear, assumed to be fixed. The ratio of the speed of rotation of the eccentric shaft about the center of the imaginary internal gear to the speed of rotation of the table carrying the inner wheel and rotating on the eccentric of the eccentric shaft about the center of the inner wheel equals the ratio of the number of teeth of the inner wheel to the difference between the number of teeth of the inernal gear and the inner wheel or that of the pitch circle radius of the inner wheel to the difference between the pitch circle radii of the internal gear and the inner wheel. The hands of rotation are opposite. According to the invention and as shown in FIG. 8 the two outermost tooth flanks of a group of teeth (which comprises two teeth in FIG. 8) which in the internal gear are enveloped by an equidistant curve from at least one cycloid are instead here defined by a circular arc which touches the equidistant curve near the tips of both teeth. The arc must be so determined that throughout the region of the tooth flanks it is the same or a greater distance away from its center than the equidistant curve defining the tooth flanks of the actual internal gear. This are K has the radius rK. Its center must clearly lie on the bisector M through the internal gear center of the groups of teeth embraced by one cycloid arc. Moreover, the centers of the radii of curvature of the cycloid I-I defining the tooth flank of the actual internal gear 1 are located on the involute S shown in FIG. 3. The involute is the locus of all centers of curvature of the cycloid. Part of the involute S is shown in FIG. 8. Since in a preferred embodiment of the invention the grinding spindle which is conducted along the cycloid H first grinds only right-hand tooth flanks during a grinding cycle and then only left-hand tooth flanks, the cusp at the apex of the involutes S in FIG. 8 is not suitable as a center for the radius of curvature of the approximating circle. The center must be a point in proximity with the intercept of the involutes S and the straight line M. A center for the approximating circle thus can be found.

Another simple and better way of finding the center of this approximating circle is to draw the tooth form of the internal gear on a much enlarged scale, inserting the bisector through the center of the internal gear of a group of teeth of the internal gear embraced by one arc of the cycloid and then finding the suitable radius rK by trial and error using a pair of dividers. This course will be adopted when, as is also possible, the equidistant curve from the hypocycloid defining the tooth profile of the internal gear touches two relatively remote tooth flanks of the end teeth of the group embraced by the cycloid arc. At least in the region of the upper halves of the teeth of the imaginary internal gear the distance of the circular arc from the equidistant curve must be as small as possible.

The tooth flanks of the internal gear are thus replaced by a grinding wheel SS (FIG. 8) which pivots about the center 0 of an equivalent circle K, the grinding wheel pivoting in such a way that the envelope curve of all positions of the grinding wheel is the circle K. The line through the axis of the grinding wheel to the center Q of the circle is marked U.

By ensuring the U always passes through the osculating point of the two pitch circles Ti and Ta, and this can be done with the aid of guide means by rotating a rod representing the line U about the center of the noneccentric part of the eccentric shaft (i.e., about the center of the pitch circle of the internal gear) at the same speed at which the eccentric shaft rotates, the grinding wheel can be made to machine the teeth of the inner wheel for as long as the latter is in mesh with the equivalent tooth contour of the internal gear represented by the circle K.

Since when the ratio of the number of teeth of the inner wheel to that of the internal gear is not equal to the ratio of the diameter of the rolling circle of the cycloid determining the shape of the teeth of the internal gear to the diameter of the relative base circle, the grinding wheel SS may machine the teeth of the inner wheel only when it is in the region of a tooth flank of the internal gear and not when it traverses the gap between two teeth of the internal gear, the grinding wheel SS must be withdrawn from the working zone perpendicularly to the plane of the drawing in FIG. 8 during each such traverse. For as long as the grinding wheel is in the region of a tooth flank of the imaginary internal gear it will machine the corresponding parts of the teeth of the inner wheel. The parts of the tooth contour of the innner wheel that are not to be ground already have been machined to a correspondingly greater depth during the roughing of the inner wheel as indicated at 40. If the inner wheel satisfies the condition that its number of teeth bears the same number of teeth of the internal gear as the rolling circle of the cylcoid defining the internal gear tooth contour to its base circle and if the individual arcs of the cycloid embrace only two neighboring teeth, then a retraction of the grinding wheel while traversing the gap between the teeth of the internal gear will be unneccessary. In such a case the wheel grinds both flanks and the crest of the tooth of the inner wheel in one pass and is withdrawn from engagement with the inner wheel blank only during return along its circular path.

Apparatus which is based on the theory that has just been explained and which is suitable for grinding the tooth flanks of the inner wheel is illustrated in FIG. 9. Parts corresponding to like parts in FIG. 7 bear the same reference numbers as the latter.

However, contrary to FIG. 7, the part 18 carries a support 41 which itself carries an arm 43 that can swivel about an axis 42. This axis corresponds to point Q and the arm corresponds to the line U in FIG. 8. The grinding wheel 44 in FIG. 9 corresponds to the grinding wheel SS in FIG. 8 and is mounted on the arm 43 at a distance C from the axis 42. The grinding wheel may be driven by a motor 45 through a gear transmission 46 and a belt 47 indicated in dot-dash lines. Moreover, a unit 48 is mounted on the arm 43 which withdraws the grinding wheel 44 upwards out of engagement with the inner wheel 2 at the appropriate times when the grinding wheel traverses a gap between two teeth of the imaginary internal gear. The arm 43 is slidably guided in a sliding block 50 which is deflectably mounted to swivel about an axis 49 (corresponding to point B in FIG. 8). The sliding block 50 is mounted on a shaft 49 in an arm 51. The arm 51 is secured on the gear wheel 19 and rotates together therewith. The distance r of the shaft 49 from the axis 52 about which the eccentric part of the eccentric shaft carrying the table 10 rotates is equal to the pitch diameter of the internal gear.

It will be understood from the foregoing explanations that the apparatus according to FIG. 9 complies with the geometrical conditions illustrated in FIG. 8.

Naturally, when work begins, the several parts must be placed into the correct angular positions. In other words, the angular position of the inner wheel blank prior to grinding not only must be adjusted to the position of the teeth, the shaft 49 that corresponds to point B in FIG. 8 must likewise be coplanar with the two axes of the eccentric shaft. Moreover, an in-feeding mechanism, not shown, for the frinding wheel 44 must be provided since the latter in practice cannot remove sufficient material from the tooth flanks of the inner wheel in a single traversing pass.

Furthermore, the withdrawal of the grinding spindle 44 from engagement with the inner wheel 2 that is to be ground must not take place until the center line of arm 43 corresponding to line U in FIG. 8 passes across the tip of an imaginary tooth of the internal gear.,This is possible because the inner wheel has been roughed with an allowance where the tips of the teeth of the internal gear engage the gap between teeth of the inner wheel, as indicated in FIG. 8 at 40. Moreover, in a kinematic reversal of the described procedure, the arm '43 may remain stationary and the work together with the machine below could be swung about point O. This has the substantial mechanical advantage of permitting the process to be performed on conventional machine tools.

Finally, it should be observed that the involute S of the cycloid H, as can be readily proved by mathematic calculation, is likewise a hypocycloid. This hypocycloid can also be generated by a gear mechanism of the kind illustrated in FIGS. 4 to 7.

It is completely synchronous with the hypocycloid generating the teeth of the internal gear. Each position of point B is associated with a particular exactly defined point on the involute S. If arrangements are made for point Q on rod U not to stand still but continuously to travel on S (FIG. 8), and this can be readily accomplished by the above described gearing, then the inner wheel can be ground by the grinding wheel SS as a precise enveloping contour of an internal gear according to the invention. However, this procedure is far more complicated than the above-described method of substituting for the internal gear an equivalent internal gear defined by circular arcs, because the pivot point 0 is then stationary.

If FIGS. 8 and 9 in the drawings are carefully considered it will be seen that the guide arm 51 and the sliding block 50 will collide with the grinding wheel 44 upon passing through the position nearest the axis 42 or point Q. In an arrangement according to FIG. 9 this cannot be avoided in the case of some relative proportions. However, the difficulty can be easily overcome in a way that will be understood from FIG. 8a. In the arrangement according to FIG. 8a the arm 51 does not rotate about the shaft 52 but about the produced axis 52' of the line connecting Q and 52. The point B which corresponds to point B in FIG. 9 rotates about this axis 52 at the end ofa radius ra which bears the same proportion to the radius ra as the distance 0-52 to to the distance 0-52. If point B is now allowed to rotate about the axis 52' at the same angular speed as previously the point B about its axis 52 then the point B which naturally must be looted on an extension of arm 43 will always remain on the same ray from point Q upon which point B moves. Hence an arm rotating about the point 52' at the end of the radius ra likewise can be provided with a slideway 49' for an extension arm 43. This arm carries the grinding wheel 44 or SS at the same distance from point Q as the guide arm 43 and the grinding wheel will thus perform the same movements as in the construction according to FIG. 9. However, from the positions of the circles K and Ta it will be understood that a collision between the grindingwheel, the arm 51, and its slideway 50 cannot occur. This form of construction is in effect merely a modification of the form of construction according to FIG. 8 which takes advantage of the theorem of sweeping rays.

FIG. 10 illustrates a cycloid which closes upon itself after two revolutions as well as a corresponding equidistant curve for the generation of the teeth of an internal gear having seven teeth. Since the number of teeth is odd the number of revolutions required for the point generating the cycloid to regain its starting point is even. For the generation of seven teeth the choice is practically limited to two revolutions. In the case of greater numbers of teeth, for example 21 teeth, as illustrated in FIG. 1 1, it is best to choose a cycloid in which the generating point does not regain the starting position until four revolutions have been completed. This avoids the teeth becoming too flat. FIG. 12 is an example of the outer wheel having 16 teeth in which the generating point on the rolling circle returns to its starting position after three complete revolutions around the base circle. From these few examples it will be understood that by choosing the number of revolutions of the rolling circle for the generation of a desired number of teeth it is possible largely to determine the shape of the teeth.

For smaller numbers of teeth two or three revolutions will usually be quite sufficient.

It follows from what has been said that the invention provides a means of producing an internally geared,

hardened, ground outer wheel and a corresponding likewise hardened and ground externally geared inner wheel by the generating roll process with a degree of precision that was not hitherto attainable.

It will be obvious to those skilled in the art that many modifications may be made within the scope of the present invention without departing from the spirit thereof, and the invention includes all such modifications.

What is claimed is:

1. In a methodof grinding the tooth flanks of an internal gear by a grinding means, the improvement comprising:

a. grinding said tooth flanks while rotating one of said grinding means and said internal gear relative to the other about the axis of said internal gear at a predetermined speed, and

b. simultaneously rotating one of said grinding means and said internal gear relative to the other about a second axis, offset from and parallel to said axis of said internal gear, at a second predetermined speed,

. said second axis and said axis of said internal gear being offset from one another by a distance equal to the difference between the length of the radius of a base circle of a cycloid and the radius of a rolling circle producing said cycloid by rolling on the interior of said base circle,

the ratio of said speed of relative rotation of said grinding means and said internal gear about said axis of said internal gear to said speed of relative rotation of said grinding means and said internal gear about said second axis being equal to the ratio of said offset distance between said second axis and said axis of said internal gear to the radius of said base circle,

e. the ratio of said radius of said rolling circle to said radius of said base circle being an aliquant fraction, the denominator of said fraction being a numeral equalto the number of teeth to be formed on said internal gear, and

g. the numerator of said fraction being a numeral from two to the difference between said number of teeth of said internal gear and two.

2. A method in accordance with claim 1 wherein the grinding means is rotated relative to the internal gear about the axis of said internal gear and relative to said internal gear about the second axis.

3. A method in accordance with claim 1 wherein the internal gear is rotated relative to the grinding means about the axis of said internal gear and relative to said grinding means about the second axis.

4. A method in accordance with claim 1 wherein all of the left-hand tooth flanks are ground and thereafter all of the right-hand tooth flanks are ground in the same way.

5. A method in accordance with claim 1 wherein all of the right-hand tooth flanks are ground and thereafter all of the left-hand tooth flanks are ground in the same way.

6. In a method of machining the tooth flanks of an external gear, adapted to mesh with an internal gear, by a hobbing means, the improvement comprising:

a. machining said tooth flanks while rotating one of said hobbing means and said external gear relative to the other about the axis of said external gear at a predetermined speed, and

b. simultaneously rotating one of said hobbing means and said external gear relative to the other about a second axis, offset from and parallel to said axis of said external gear, at a predetermined speed,

c. said second axis and said axis of said external gear being offset from one another by a distance equal to the difference between the radius of the pitch circle of said internal gear and the radius of the pitch circle of said external gear,

d. the ratio of said speed of relative rotation of said hobbing means and said external gear about said axis of said external gear to said speed of relative rotation of said hobbing means and said external gear about said second axis being equal to the ratio of said difference between said radius of said pitch circle of said internal gear and said radius of said pitch circle of said external gear to said radius of said pitch circle of said external gear, and,

e. said rotation about said axis of said external gear and said rotation about said second axis being opposite in direction.

7. A method in accordance with claim 6 wherein the hobbing means is rotated relative to the external gear about the axis of said external gearand relative to said external gear about the second axis.

8. A method in accordance with claim 6 wherein the external gear is rotated relative to the hobbing means about the axis of said external gera and relative to said hobbing means about the second axis.

9. A method in accordance with claim 8 wherein the hobbing means is a shaping tool in the form of at least part of the contour of the teeth of the internal gear, is reciprocated parallel to the axes of rotation and performs no movement in a plane normal to the second axis other than the necessary infeed motion to allow for the gradual removal of material.

10. A method in accordance with claim 8 wherein the hobbing means is a grinding wheel having an axis paral- 6 approximates the contours of the two outermost flanks of a group of at least two adjacent teeth of the internal gear, the center of the internal contour of said internal gear coincides with the second axis, the radius line from the center of said arc through said grinding wheel always passing through a point on the pitch circle of said external gear, and said point always lies on a radius line of said second axis through said axis of said external gear.

11. A method in accordance with claim 10 wherein the grinding wheel, after traversing a part of the arc, corresponding to a first one of the two tooth flank contours, is disengaged from the external gear by displacement in the direction of the axis of said grinding wheel and, after having traversed the gap between said contours of said two flanks, is reengaged with said external gear, and these steps are repeated until all the teeth flanks of said external gear are ground.

12. A method in accordance with claim 10 wherein the external gear has an odd number of teeth, the ratio of said odd number of teeth to the number of teeth of the internal gear is equal to the ratio of a rolling circle producing a cycloid by rolling on the interior of the base circle of said cycloid and the radius of said base circle, the grinding wheel is moved along the arc about the center of said are in the same direction as the direction of rotation of said external gear about its axis, a tooth flank is ground on the trailing side of a tooth during said movement, said grinding wheel is axially disengaged from said external gear, said grinding wheel is reengaged with said external gear, when said grinding wheel has reached the next tooth space of said external gear, the leading flank of the tooth trailing said space is ground, said grinding wheel is disengaged from said external gear, said grinding wheel is moved back along said are to a position where it can be engaged with the tooth space trailing after said next tooth space, said trailing tooth space having in the meantime reached a position in which said grinding wheel can be engaged with the trailing flank of the tooth between said next tooth space and said trailing tooth space, and the grinding wheel is reengaged with the last mentioned tooth flank, and these steps are repeated until all the tooth flanks of said external gear are ground.

13. Apparatus for grinding the tooth flanks of an internal gear comprising:

a. base means,

b. eccentric shaft means comprising two integral shaft parts offset from and parallel to each other,

c. a first one of said two shaft parts is rotatably mounted on said base means,

d. table means rotatably mounted on the second one of said two shaft parts and adapted to fixedly hold said internal gear to be ground so that the axis of said internal gear coincides with the axis of said second shaft part,

e. driving means for rotating said eccentric shaft means,

f. an external gear ring fixedly mounted on said base means concentrically surrounding said first shaft part,

g. an internal gear ring fixedly mounted on said table means concentrically with respect to said second shaft part,

h. said second shaft part carrying in a mounting means, a plurality of gears meshing with each other,

i. one of said gears meshing with said external gear ring and the other of said gears meshing with said internal gear ring, and

j. grinding means rotatably mounted on said base means so that it can engage said tooth flanks.

14. A gear grinding apparatus in accordance with claim 13 wherein the offset of the eccentric shaft is equal to the difference between the radius of a base circle of a cycloid and the radius of a rolling circle producing said cycloid by rolling on the interior of said base circle, the ratio of the radius of said rolling circle to the radius of said base circle is an aliquant fraction, the denominator of said fraction is a numeral equal to the number of teeth of said internal gear, the numerator of said fraction is a numeral from at least two to the difference between the number of teeth of said internal gear and two, and the ratio of the speed of rotation of said eccentric shaft to the speed of rotation of said table is equal to the ratio of said radius of said base circle to the difference between said radius of said base circle and said radius of said rolling circle.

15. Apparatus in accordance with claim 14 wherein the grinding element is displaceable in the peripheral direction with respect to the eccentric shaft means.

16. Apparatus for machining the teeth of an external gear adapted to mesh with an internal gear, comprising:

a. base means,

b. eccentric shaft means comprising two integral shaft parts, offset from and parallel to each other,

c. the second one of said two shaft parts being rotatably mounted in said base means,

d. table means rotatably mounted on the first of said two shaft parts and adapted to fixedly hold said external gear to be machined so that the axis of said external gear coincides with the axis of said first shaft part,

e. driving means for rotating said eccentric shaft,

f. an external gear ring fixedly mounted on said table and concentrically surrounding said first shaft part,

g. an internal gear ring fixedly mounted on said base means concentrically with respect to said second shaft part,

h. said second shaft part carrying, in a mounting means, a plurality of gears meshing with each other,

i. one of said gears meshing with said external gear ring and the other of said gears meshing with said internal gear ring, and

j. machining means mounted on said base means and adapted to machine the teeth of said external gear.

17. A grinding apparatus in accordance with claim 16 wherein the offset of the eccentric shaft is equal to the difference between the radius of the pitch circle of the internal gear and the radius of the pitch circle of the external gear, and the ratio of the speed of rotation of said eccentric shaft to the speed of rotation of the rotatable table is equal to the ratio of the radius of said pitch circle of said external gear to the difference between said radius of said pitch circle of said internal gear and said radius of said pitch circle of said external gear.

18. Apparatus in accordance with claim 16 wherein the machining means includes a tool-shaped according to at least a portion of the profile of the internal gear.

19. Apparatus in accordance with claim 16 wherein the machining means includes a grinding wheel mounted on an arm pivotable about an axis fixed in relation to the base means and parallel to the axis of the eccentric shaft, said axis of said arm being offset from the axis of the first shaft part at a distance such that a circular arc about said axis of said arm approximates and envelops the contours of two tooth flanks of the internal gear, the center of the internal contour of said internal gear coincides with the axis of the second shaft part, and said grinding wheel is mounted such that its enveloping curve during pivoting about said axis of said arm traverses said circular arc, and means for axially displacing said grinding wheel into engagement and out of engagement with said external gear, said arm being slidably guided in ways rotating synchroneously with said first shaft part around said axis of said second shaft part, said ways lying in the plane containing the axes of said two shaft parts, and the radius of the circle on which said ways rotates around said axis of said second shaft part being equal to said radius of the pitch circle of said internal gear.

20. Apparatus in accordance with claim 17 wherein the circular arc approximates and envelops the contour of two relatively remote tooth flanks of two neighboring teeth of the internal gear.

, UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 3 ,"782 04o ated January 1, 1974 Inventor(s) Hermann Harle; Siegfried Eisenmann It is. certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:

Column 20, line 22, after "ratio of", insert the radius Column 20, line 65 after "carrying", insert (comma) Signed. and sealed this lOth'clay off December 197 (SEAL) Attest: v

MCCOY M. GIBSON JR. C. MARSHALL DANN Atte'sting Officer a Commissioner of Patents FORM PO10 (1 uscoMM-oc 60376-P69 fl' UTS. GOVERNMENT PRINTING OFFICE: 1969 O3$5-334, 

1. In a method of grinding the tooth flanks of an internal gear by a grinding means, the improvement comprising: a. grinding said tooth flanks while rotating one of said grinding means and said internal gear relative to the other about the axis of said internal gear at a predetermined speed, and b. simultaneously rotating one of said grinding means and said internal gear relative to the other about a second axis, offset from and parallel to said axis of said internal gear, at a second predetermined speed, c. said second axis and said axis of said internal gear being offset from one another by a distance equal to the difference between the length of the radius of a base circle of a cycloid and the radius of a rolling circle producing said cycloid by rolling on the interior of said base circle, the ratio of said speed of relative rotation of said grinding means and said internal gear about said axis of said internal gear to said speed of relative rotation of said grinding means and said internal gear about said second axis being equal to the ratio of said offset distance between said second axis and said axis of said internal gear to the radius of said base circle, e. the ratio of said radius of said rolling circle to said radius of said base circle being an aliquant fraction, f. the denominator of said fraction being a numeral equal to the number of teeth to be formed on said internal gear, and g. the numerator of said fraction being a numeral from two to the difference between said number of teeth of said internal gear and two.
 2. A method in accordance with claim 1 wherein the grinding means is rotated relative to the internal gear about the axis of said internal gear and relative to said internal gear about the second axis.
 3. A method in accordance with claim 1 wherein the internal gear is rotated relative to the grinding means about the axis of said internal gear and relative to said grinding means about the second axis.
 4. A method in accordance with claim 1 wherein all of the left-hand tooth flanks are ground and thereafter all of the right-hand tooth flanks are ground in the same way.
 5. A method in accordance with claim 1 wherein all of the right-hand tooth flanks are ground and thereafter all of the left-hand tooth flanks are ground in the same way.
 6. In a method of machining the tooth flanks of an external gear, adapted to mesh with an internal gear, by a hobbing means, the improvement comprising: a. machining said tooth flanks while rotating one of said hobbing means and said external gear relative to the other about the axis of said external gear at a predetermined speed, and b. simultaneously rotating one of said hobbing means and said external gear relative to the other about a second axis, offset from and parallel to said axis of said external gear, at a predetermined speed, c. said second axis and said axis of said external gear being offset from one another by a distance equal to the difference between the radius of the pitch circle of said internal gear and the radius of the pitch circle of said external gear, d. the ratiO of said speed of relative rotation of said hobbing means and said external gear about said axis of said external gear to said speed of relative rotation of said hobbing means and said external gear about said second axis being equal to the ratio of said difference between said radius of said pitch circle of said internal gear and said radius of said pitch circle of said external gear to said radius of said pitch circle of said external gear, and, e. said rotation about said axis of said external gear and said rotation about said second axis being opposite in direction.
 7. A method in accordance with claim 6 wherein the hobbing means is rotated relative to the external gear about the axis of said external gear and relative to said external gear about the second axis.
 8. A method in accordance with claim 6 wherein the external gear is rotated relative to the hobbing means about the axis of said external gear and relative to said hobbing means about the second axis.
 9. A method in accordance with claim 8 wherein the hobbing means is a shaping tool in the form of at least part of the contour of the teeth of the internal gear, is reciprocated parallel to the axes of rotation and performs no movement in a plane normal to the second axis other than the necessary infeed motion to allow for the gradual removal of material.
 10. A method in accordance with claim 8 wherein the hobbing means is a grinding wheel having an axis parallel to the axis of the external gear, said grinding wheel is reciprocated along a circular arc in a plane normal to said axis of said external gear, said arc envelops and approximates the contours of the two outermost flanks of a group of at least two adjacent teeth of the internal gear, the center of the internal contour of said internal gear coincides with the second axis, the radius line from the center of said arc through said grinding wheel always passing through a point on the pitch circle of said external gear, and said point always lies on a radius line of said second axis through said axis of said external gear.
 11. A method in accordance with claim 10 wherein the grinding wheel, after traversing a part of the arc, corresponding to a first one of the two tooth flank contours, is disengaged from the external gear by displacement in the direction of the axis of said grinding wheel and, after having traversed the gap between said contours of said two flanks, is reengaged with said external gear, and these steps are repeated until all the teeth flanks of said external gear are ground.
 12. A method in accordance with claim 10 wherein the external gear has an odd number of teeth, the ratio of said odd number of teeth to the number of teeth of the internal gear is equal to the ratio of a rolling circle producing a cycloid by rolling on the interior of the base circle of said cycloid and the radius of said base circle, the grinding wheel is moved along the arc about the center of said arc in the same direction as the direction of rotation of said external gear about its axis, a tooth flank is ground on the trailing side of a tooth during said movement, said grinding wheel is axially disengaged from said external gear, said grinding wheel is reengaged with said external gear, when said grinding wheel has reached the next tooth space of said external gear, the leading flank of the tooth trailing said space is ground, said grinding wheel is disengaged from said external gear, said grinding wheel is moved back along said arc to a position where it can be engaged with the tooth space trailing after said next tooth space, said trailing tooth space having in the meantime reached a position in which said grinding wheel can be engaged with the trailing flank of the tooth between said next tooth space and said trailing tooth space, and the grinding wheel is reengaged with the last mentioned tooth flank, and these steps are repeated until all the tooth flanks of said external gear are ground.
 13. Apparatus for grinding the tooth flanks of an iNternal gear comprising: a. base means, b. eccentric shaft means comprising two integral shaft parts offset from and parallel to each other, c. a first one of said two shaft parts is rotatably mounted on said base means, d. table means rotatably mounted on the second one of said two shaft parts and adapted to fixedly hold said internal gear to be ground so that the axis of said internal gear coincides with the axis of said second shaft part, e. driving means for rotating said eccentric shaft means, f. an external gear ring fixedly mounted on said base means concentrically surrounding said first shaft part, g. an internal gear ring fixedly mounted on said table means concentrically with respect to said second shaft part, h. said second shaft part carrying in a mounting means, a plurality of gears meshing with each other, i. one of said gears meshing with said external gear ring and the other of said gears meshing with said internal gear ring, and j. grinding means rotatably mounted on said base means so that it can engage said tooth flanks.
 14. A gear grinding apparatus in accordance with claim 13 wherein the offset of the eccentric shaft is equal to the difference between the radius of a base circle of a cycloid and the radius of a rolling circle producing said cycloid by rolling on the interior of said base circle, the ratio of the radius of said rolling circle to the radius of said base circle is an aliquant fraction, the denominator of said fraction is a numeral equal to the number of teeth of said internal gear, the numerator of said fraction is a numeral from at least two to the difference between the number of teeth of said internal gear and two, and the ratio of the speed of rotation of said eccentric shaft to the speed of rotation of said table is equal to the ratio of said radius of said base circle to the difference between said radius of said base circle and said radius of said rolling circle.
 15. Apparatus in accordance with claim 14 wherein the grinding element is displaceable in the peripheral direction with respect to the eccentric shaft means.
 16. Apparatus for machining the teeth of an external gear adapted to mesh with an internal gear, comprising: a. base means, b. eccentric shaft means comprising two integral shaft parts, offset from and parallel to each other, c. the second one of said two shaft parts being rotatably mounted in said base means, d. table means rotatably mounted on the first of said two shaft parts and adapted to fixedly hold said external gear to be machined so that the axis of said external gear coincides with the axis of said first shaft part, e. driving means for rotating said eccentric shaft, f. an external gear ring fixedly mounted on said table and concentrically surrounding said first shaft part, g. an internal gear ring fixedly mounted on said base means concentrically with respect to said second shaft part, h. said second shaft part carrying, in a mounting means, a plurality of gears meshing with each other, i. one of said gears meshing with said external gear ring and the other of said gears meshing with said internal gear ring, and j. machining means mounted on said base means and adapted to machine the teeth of said external gear.
 17. A grinding apparatus in accordance with claim 16 wherein the offset of the eccentric shaft is equal to the difference between the radius of the pitch circle of the internal gear and the radius of the pitch circle of the external gear, and the ratio of the speed of rotation of said eccentric shaft to the speed of rotation of the rotatable table is equal to the ratio of the radius of said pitch circle of said external gear to the difference between said radius of said pitch circle of said internal gear and said radius of said pitch circle of said external gear.
 18. Apparatus in accordance with claim 16 wherein the machining means includes a tool-shaped according to at least a portion oF the profile of the internal gear.
 19. Apparatus in accordance with claim 16 wherein the machining means includes a grinding wheel mounted on an arm pivotable about an axis fixed in relation to the base means and parallel to the axis of the eccentric shaft, said axis of said arm being offset from the axis of the first shaft part at a distance such that a circular arc about said axis of said arm approximates and envelops the contours of two tooth flanks of the internal gear, the center of the internal contour of said internal gear coincides with the axis of the second shaft part, and said grinding wheel is mounted such that its enveloping curve during pivoting about said axis of said arm traverses said circular arc, and means for axially displacing said grinding wheel into engagement and out of engagement with said external gear, said arm being slidably guided in ways rotating synchroneously with said first shaft part around said axis of said second shaft part, said ways lying in the plane containing the axes of said two shaft parts, and the radius of the circle on which said ways rotates around said axis of said second shaft part being equal to said radius of the pitch circle of said internal gear.
 20. Apparatus in accordance with claim 17 wherein the circular arc approximates and envelops the contour of two relatively remote tooth flanks of two neighboring teeth of the internal gear. 